{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:FHPXQEUJFM3CFK2XWJCVY6TT3M","short_pith_number":"pith:FHPXQEUJ","schema_version":"1.0","canonical_sha256":"29df7812892b3622ab57b2455c7a73db1ac56ed659ef2b046812447ffe382e4e","source":{"kind":"arxiv","id":"1502.04620","version":2},"attestation_state":"computed","paper":{"title":"On the exact region determined by Kendall's tau and Spearman's rho","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Manuela Schreyer, Roland Paulin, Wolfgang Trutschnig","submitted_at":"2015-02-16T16:44:49Z","abstract_excerpt":"Using properties of shuffles of copulas and tools from combinatorics we solve the open question about the exact region $\\Omega$ determined by all possible values of Kendall's $\\tau$ and Spearman's $\\rho$. In particular, we prove that the well-known inequality established by Durbin and Stuart in 1951 is only sharp on a countable set with sole accumulation point $(-1,-1)$, give a simple analytic characterization of $\\Omega$ in terms of a continuous, strictly increasing piecewise concave function, and show that $\\Omega$ is compact and simply connected but not convex. The results also show that fo"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1502.04620","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-02-16T16:44:49Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"9fe6e149f2c29052591a3fee7daffd3fc99e04fb07152aef08da919a9fed03a6","abstract_canon_sha256":"d4a6e0de89e5aa2047eee336c4fa9a0d643c2b52ef3260c7fac7b15a49377013"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:04.712258Z","signature_b64":"rLUI7ongGkGpSNGsAs41X+AdLrEqmaXey9+regnJd/09APlMBtOXhBBx0NclMOgqUImHJd+BhjuxML9UcT/zBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29df7812892b3622ab57b2455c7a73db1ac56ed659ef2b046812447ffe382e4e","last_reissued_at":"2026-05-18T00:46:04.711748Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:04.711748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the exact region determined by Kendall's tau and Spearman's rho","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Manuela Schreyer, Roland Paulin, Wolfgang Trutschnig","submitted_at":"2015-02-16T16:44:49Z","abstract_excerpt":"Using properties of shuffles of copulas and tools from combinatorics we solve the open question about the exact region $\\Omega$ determined by all possible values of Kendall's $\\tau$ and Spearman's $\\rho$. In particular, we prove that the well-known inequality established by Durbin and Stuart in 1951 is only sharp on a countable set with sole accumulation point $(-1,-1)$, give a simple analytic characterization of $\\Omega$ in terms of a continuous, strictly increasing piecewise concave function, and show that $\\Omega$ is compact and simply connected but not convex. The results also show that fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04620","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1502.04620","created_at":"2026-05-18T00:46:04.711835+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.04620v2","created_at":"2026-05-18T00:46:04.711835+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04620","created_at":"2026-05-18T00:46:04.711835+00:00"},{"alias_kind":"pith_short_12","alias_value":"FHPXQEUJFM3C","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"FHPXQEUJFM3CFK2X","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"FHPXQEUJ","created_at":"2026-05-18T12:29:19.899920+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FHPXQEUJFM3CFK2XWJCVY6TT3M","json":"https://pith.science/pith/FHPXQEUJFM3CFK2XWJCVY6TT3M.json","graph_json":"https://pith.science/api/pith-number/FHPXQEUJFM3CFK2XWJCVY6TT3M/graph.json","events_json":"https://pith.science/api/pith-number/FHPXQEUJFM3CFK2XWJCVY6TT3M/events.json","paper":"https://pith.science/paper/FHPXQEUJ"},"agent_actions":{"view_html":"https://pith.science/pith/FHPXQEUJFM3CFK2XWJCVY6TT3M","download_json":"https://pith.science/pith/FHPXQEUJFM3CFK2XWJCVY6TT3M.json","view_paper":"https://pith.science/paper/FHPXQEUJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.04620&json=true","fetch_graph":"https://pith.science/api/pith-number/FHPXQEUJFM3CFK2XWJCVY6TT3M/graph.json","fetch_events":"https://pith.science/api/pith-number/FHPXQEUJFM3CFK2XWJCVY6TT3M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FHPXQEUJFM3CFK2XWJCVY6TT3M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FHPXQEUJFM3CFK2XWJCVY6TT3M/action/storage_attestation","attest_author":"https://pith.science/pith/FHPXQEUJFM3CFK2XWJCVY6TT3M/action/author_attestation","sign_citation":"https://pith.science/pith/FHPXQEUJFM3CFK2XWJCVY6TT3M/action/citation_signature","submit_replication":"https://pith.science/pith/FHPXQEUJFM3CFK2XWJCVY6TT3M/action/replication_record"}},"created_at":"2026-05-18T00:46:04.711835+00:00","updated_at":"2026-05-18T00:46:04.711835+00:00"}